From the N-Body Schrödinger Equation to the Vlasov Equation

François Golse (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

This paper describes a method for obtaining an estimate of the convergence rate for the joint mean-field and semiclassical limit of the N-particle Schrödinger equation leading to the Vlasov equation. The interaction force is assumed to be Lipschitz continuous. This is an account of a recent work in collaboration with T. Paul [Arch. Ration. Mech. Anal. 223 (2017), 57-94].

Mots clés: Mean-field limit; Vlasov equation; Schrödinger equation; Wasserstein distance; Töplitz operator

Domaines: Equations aux dérivées partielles [math.AP]

François Golse. From the N-Body Schrödinger Equation to the Vlasov Equation. From Particle Systems to Partial Differential Equations, Dec 2015, Braga, Portugal. pp.199-219, ⟨10.1007/978-3-319-66839-0_10⟩. ⟨hal-01721122⟩